Apparatus and method of processing polynomials

Abstract

An apparatus of processing polynomials includes at least one reconfigurable module and an encoder controller. The reconfigurable module includes a plurality of linear feedback shift registers. The encoder controller can control the reconfigurable module to factor a generator polynomial into a factorial polynomial. In the reconfigurable module, the linear feedback shift registers can register a plurality of factors of the factorial polynomial respectively.

What is claimed is: 
     
       1. An apparatus of processing polynomials, the apparatus comprising:
 at least one reconfigurable module including a plurality of linear feedback shift registers to receive input data respectively; and 
 an encoder controller for controlling the reconfigurable module to factor a generator polynomial based on the input data into a factorial polynomial, the linear feedback shift registers for registering a plurality of factors of the factorial polynomial respectively, and the encoder controller having an output fed back to the reconfigurable module. 
 
     
     
       2. The apparatus of  claim 1 , wherein the encoder controller essentially consists of a plurality of adders associated with the linear feedback shift registers, wherein the adders and the reconfigurable module constitute a single mode encoder. 
     
     
       3. The apparatus of  claim 1 , wherein the encoder controller essentially consists of a plurality of adders associated with the linear feedback shift registers and a multiplexer configured to select one of the linear feedback shift registers to control varied modes of an encoding process, wherein the adders, the multiplexer and the reconfigurable module constitute a multi-mode encoder. 
     
     
       4. The apparatus of  claim 1 , further comprising:
 means for assisting the linear feedback shift registers in using the factors of the factorial polynomial to calculate syndromes; 
 a key equation solver for generating an error location polynomial based on the syndromes; and 
 means for assisting the reconfigurable module and the means for assisting the linear feedback shift registers in executing a Chien search for searching all roots of the error location polynomial according to the factors, so as to find an error location. 
 
     
     
       5. An apparatus of processing polynomials, the apparatus comprising:
 at least one reconfigurable module including a plurality of linear feedback shift registers to receive input data respectively; and 
 means for controlling the reconfigurable module to factor a generator polynomial based on the input data into a factorial polynomial, the linear feedback shift registers for registering a plurality of factors of the factorial polynomial respectively, and the controlling means having an output fed back to the reconfigurable module. 
 
     
     
       6. The apparatus of  claim 5 , wherein the controlling means includes means for using the reconfigurable module to perform a single mode of the encoding process. 
     
     
       7. The apparatus of  claim 5 , wherein the controlling means includes means for selecting one of the linear feedback shift registers to control varied modes of an encoding process. 
     
     
       8. The apparatus of  claim 5 , further comprising:
 means for assisting the linear feedback shift registers in using the factors of the factorial polynomial to calculate syndromes; 
 a key equation solver for generating an error location polynomial based on the syndromes; and 
 means for assisting the reconfigurable module and the means for assisting the linear feedback shift registers in executing a Chien search for searching all roots of the error location polynomial according to the factors, so as to find an error location. 
 
     
     
       9. A method of processing polynomials in a computer system, the method comprising:
 (a) providing at least one reconfigurable module including a plurality of linear feedback shift registers to receive input data respectively; and 
 (b) utilizing an encoder controller for controlling the reconfigurable module to factor a generator polynomial based on the input data into a factorial polynomial, so as to register a plurality of factors of the factorial polynomial in the linear feedback shift registers, respectively, and the encoder controller having an output fed back to the reconfigurable module. 
 
     
     
       10. The method of  claim 9 , wherein the step (b) comprises:
 using the reconfigurable module to perform a single mode of the encoding process. 
 
     
     
       11. The method of  claim 9 , wherein the step (b) comprises:
 selecting one of the linear feedback shift registers to control varied modes of an encoding process. 
 
     
     
       12. The method of  claim 9 , further comprising:
 (c) calculating syndromes based on the factors of the factorial polynomial; 
 (d) generating an error location polynomial based on the syndromes, and 
 (e) using the factors to search all roots of the error location polynomial, so as to find an error location. 
 
     
     
       13. The method of  claim 12 , wherein the step (c) comprises:
 utilizing a plurality of basis transformers electrically coupled with the linear feedback shift registers respectively for using the factors of the factorial polynomial to calculate syndromes. 
 
     
     
       14. The method of  claim 13 , wherein the step (e) comprises:
 utilizing a plurality of inverse basis transformers electrically coupled with the linear feedback shift registers respectively, the reconfigurable module and the basis transformers to execute a Chien search for searching said all roots of the error location polynomial according to the factors, so as to find the error location. 
 
     
     
       15. The method of  claim 12 , wherein the step (e) comprises:
 utilizing a plurality of inverse basis transformers electrically coupled with t the linear feedback shift registers respectively, the reconfigurable module and the basis transformers to execute a Chien search for searching said all roots of the error location polynomial according to the factors, so as to find the error location. 
 
     
     
       16. The method of  claim 9  in which the computer system is a storage element or a communications system.